Question

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Answer 1

Answer:

Ok, I have done

Step-by-step explanation:

Answer 2

We have :-

$= > x^{2} + \frac{1}{ {x}^{2} } = 51 \: \: \: .....(1)$

On multiplying equation (1) by x, we get :

$= > {x}^{3} + \frac{1}{x} = 51x \\ \\ = > {x}^{3} = 51x - \frac{1}{x} \: \: \: .....(2)$

Similarly, on dividing equation (1) by x, we get :

$= > x + \frac{1}{ {x}^{3} } = \frac{51}{x} \\ \\ = > \frac{1}{ {x}^{3} } = \frac{51}{x} - x \: \: \: .....(3)$

Now, subtract equation (2) and equation (3) :

$= > {x}^{3} - \frac{1}{ {x}^{3} } = 51x - \frac{1}{x} - \frac{51}{x} + x \\ \\ = > {x}^{3} - \frac{1}{ {x}^{3} } = 51(x - \frac{1}{x} ) + (x - \frac{1}{x} ) \\ \\ = > {x}^{3} - \frac{1}{ {x}^{3} } = 52(x - \frac{1}{x} ) \: \: \: .....(4)$

Then,

$= > {x}^{2} + \frac{1}{ {x}^{2} } = 51 \\ \\ = > {x}^{2} + \frac{1}{x^{2} } - 2 = 49 \\ \\ = > (x - \frac{1}{x} )^{2} = 49 \\ \\ = > x - \frac{1}{x} = ± 7 \: \: \: .....(5)$

Thus, from equations (4) and (5) :-

=> x³ - 1/x³ = 52(±7) = ± 364

Since, this method is quite a bit lengthy, you can also use the identity :-

a³ - b³ = (a - b)(a² + ab + b²)

Hope, it'll help you.....